Related papers: About Algorithm for Transformation of Logic Functi…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
The Edinburgh Logical Framework (LF) is a dependently type lambda calculus that can be used to encode formal systems. The versatility of LF allows specifications to be constructed also about the encoded systems. The Twelf system exploits…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
Artificial Intelligence agents are required to learn from their surroundings and to reason about the knowledge that has been learned in order to make decisions. While state-of-the-art learning from data typically uses sub-symbolic…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
There is growing excitement about building software verifiers, synthesizers, and other Automated Reasoning (AR) tools by combining traditional symbolic algorithms and Large Language Models (LLMs). Unfortunately, the current practice for…
Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs…
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.
There have been a huge number of benchmarks proposed to evaluate how large language models (LLMs) behave for logic inference tasks. However, it remains an open question how to properly evaluate this ability. In this paper, we provide a…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
Large Language Models (LLMs) have demonstrated impressive real-world utility, exemplifying artificial useful intelligence (AUI). However, their ability to reason adaptively and robustly -- the hallmarks of artificial general intelligence…
Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s.…
A number of extensions exist for Alternating-time Temporal Logic; some of these mix strategies and partial observability but, to the best of our knowledge, no work provides a unified framework for strategies, partial observability and…
We consider state of the art applications of artificial intelligence (AI) in modelling human financial expectations and explore the potential of quantum logic to drive future advancements in this field. This analysis highlights the…
Translating natural language (NL) into a formal language such as temporal logic (TL) is integral for human communication with robots and autonomous systems. State-of-the-art approaches decompose the task into a lifting of atomic…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
Logic programming is a powerful paradigm for programming autonomous agents in dynamic domains, as witnessed by languages such as Golog and Flux. In this work we present ALPprolog, an expressive, yet efficient, logic programming language for…